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Decomposition is needed when:

• You have a single-plane balancing result but the rotor has two correction planes
• The calculated total correction needs to be distributed physically
• You're converting a single-plane measurement to a two-plane correction

This is common for rotors where the unbalance is primarily static (disc-like rotors) but two planes are available for correction.

Static unbalance — a single unbalance vector that displaces the principal inertia axis parallel to the rotation axis. Both planes get corrections at the same angle.

Couple unbalance — two equal and opposite unbalance vectors that tilt the principal inertia axis. The planes get corrections at opposite angles (180° apart).

Most real rotors have a combination (dynamic unbalance) requiring full two-plane balancing.

The CG position determines the lever ratio:

• CG centered (L₁ = L₂): 50/50 split
• CG closer to Plane 1 (L₁ < L₂): Plane 1 gets less mass, Plane 2 gets more
• CG at Plane 1 (L₁ = 0): All correction goes to Plane 1

The formula: m₁ = m_total × L₂/(L₁+L₂) — the plane farther from CG gets more of the share.

Measure axially along the shaft from the center of gravity to each correction plane:

• Use rotor drawings for CG location, or find CG experimentally on knife edges
• Correction plane = the axial location where you attach weights
• L₁ = distance from CG to Plane 1
• L₂ = distance from CG to Plane 2

For symmetrical rotors, the CG is at the geometric center.

Guidelines:

• Single-plane: L/D ratio < 0.5, disc-like rotors, primarily static unbalance
• Two-plane: L/D ratio > 0.5, long rotors, significant couple unbalance
• Two-plane: When single-plane doesn't achieve the required quality
• Two-plane: Rotors near or above critical speed

When in doubt, two-plane balancing is always more thorough.